In a village just north of Baghdad, three policemen were killed and 10 were wounded when a car bomb exploded near their checkpoint.
And in the southwestern suburbs of Baghdad, a roadside bomb struck a car carrying anti-al-Qaida Sunni fighters, killing two and wounding three, police and hospital officials said.
The Sunni militia group, known as the Sahwa, joined forces with U.S. troops at the height of the Iraq war to fight al-Qaida. Since then, Sahwa members have been a frequent target for Sunni insurgents, who call the militiamen traitors.
Hospital officials confirmed the casualty figures for all the attacks. All officials spoke on condition of anonymity because they were not authorized to talk to the media.
There was no immediate claim of responsibility for Monday's attacks, but insurgent groups frequently target civilians in cafes and public areas, as well as members of the security forces, in an attempt to undermine confidence in the Shiite-led government and stir up Iraq's already simmering sectarian tensions.
The attacks came a day after a series of bombings in and around Baghdad killed at least 39 people.
At least 150 people have died in attacks across the country so far this month, according to an Associated Press count.